Answer:
The force magnitude is
and it is directed at 57.98° from the horizontal in a counterclockwise manner.
Explanation:
The problem states that
At t = 0,
The angular rate of increase is
Converting to revolutions per second gives us
The rope length is defined by
At , Tension T of the rope is 18 kN.
The weight of the para-sailor is
In analyzing the question, we observe that the equation for length can be represented as a linear displacement equation.
The derivative of displacement results in velocity.
Hence,
signifies the velocity, and further differentiation yields acceleration.
Therefore,
Now considering the moment when the rope forms a 30° angle with the water,
typically angular velocity is expressed as
where represents the angular displacement.
Next, evaluating the interval from gives us
making t the focal point.
At this time, the displacement measures
The linear velocity computes to
Whereas linear acceleration calculates as
Generally, radial acceleration is given by
Simultaneously, angular acceleration can be represented as
Then
Thus,
The resultant acceleration is mathematically denoted as
Now the acceleration's direction is mathematically expressed as
The y-axis force acting on the para-sailor is mathematically shown as
The x-axis force acting on the para-sailor is represented as
The overall force is calculated as
The directional force is evaluated as